A cup of coffee has temperature (in ) that changes according to

MATHEMATICS · Single correct · AP · Calculus BC · Differential Equations · Differential Equations

Problem

A cup of coffee has temperature

T

(in

^{\circ}\!\text{C}

) that changes according to

\dfrac{dT}{dt}=-0.03\,(T-20)

, where

t

is measured in minutes and the surrounding room temperature is

20^{\circ}\!\text{C}

. If

T(0)=90

, which of the following is the BEST estimate of the coffee’s temperature after

10

minutes obtained by two equal tangent-line steps of

5

minutes each? (a)

79.5^{\circ}\!\text{C}

(b)

70.6^{\circ}\!\text{C}

(c)

73.5^{\circ}\!\text{C}

(d)

62.4^{\circ}\!\text{C}